iCloud won't sync to new Apple ID
Because of unauthorized activity on my account, I recently changed my Apple ID and Password. Now my iMac continually receive notices from iCloud that I can't access the service. iCloud seems insistent on retaining my old ID and Password, and I can't find any way to change its references in the System Preferences. I can, however go to icloud.com and be automatically connected to my iCloud account.
I've tried deleting any KeyChain references to iCloud, but that doesn't seem to help either. When I go to System Preferences > Internet Accounts and try to update my iCloud settings, I'm immediate presented with my old ID and asked for my old Password. That's as far as I can get.
The continual notifications from iCloud are driving me nuts. If anything, can someone tell me how to turn them off?
Thanks.
iMac, OS X Yosemite (10.10.4), 21-inch, 2012 model